In optical data transmission, digital data may be transmitted by means of an optical transmission signal. The optical transmission signal is generated, by modulating the phase of an optical carrier signal, which possesses a carrier frequency, in dependence on the transmitted data values and in accordance with a constellation diagram of a respective phase-shift keying (PSK) modulation method. Each point of the constellation diagram represents a finite set of data bits that are to be transmitted. Such a set of data bits is called a data symbol. A data symbol is represented by a corresponding constellation point of a constellation diagram, wherein the constellation point has a corresponding symbol phase value. Depending on the data symbols that are to be transmitted, respective constellation points and symbol phase values are derived. The phase of the optical carrier signal is modulated, such that it corresponds to the derived symbol phase values representing the transmitted data symbols.
An example for a phase-shift keying modulation method is Binary Phase-Shift Keying (BPSK), in which each point of the corresponding constellation diagram represents one bit and in which adjacent constellation points are separated by a separation angle that has an absolute value of π. Another example of a phase-shift keying modulation methods is Quadrature Phase-Shift Keying (QPSK), in which each constellation point represents two bits and in which adjacent constellation points are separated by a separation angle that has an absolute value of π/2.
At a receiving side, data detection may be carried out using a coherent reception scheme: the received optical transmission signal is mixed with a coherent optical signal that possesses the carrier frequency and a phase, which is ideally equal to the phase of the optical carrier signal. This mixing yields a resulting optical baseband signal. The optical baseband signal is converted to a sampled electrical signal via analogue-digital conversion, and the phase of the sampled electrical signal is estimated for deriving received data values. Using a hard-decision detection scheme, it is decided for that point of the constellation diagram, whose symbol phase value is most similar to the estimated phase of the received optical carrier signal. From the estimated symbol phase values corresponding data symbols and corresponding data valued are then derived.
When transmitting optical signals over a non-ideal optical transmission channel, the phase of the transmitted optical carrier signal may be changed due to transmission distortions caused by linear and/or non-linear effects of the optical transmission channel. The phase of the optical transmission signal may be changed by an absolute phase error that is greater than half of the separation angle of the constellation diagram. The result of such a phase error in combination with hard decision detection would be false estimated symbol phase values and thus false derived data values for the amount of time, for which the phase error remains to exceed half of the separation angle. If the data values are for example data bits, then false estimated symbol phase values caused by such a phase error may result in bit inversion of one ore more data bits represented by a data symbol.
A common technique to compensate transmission errors caused by phase errors of the transmission channel is the technique of differential coding. On the transmission side, the derived data symbols are differentially encoded into differentially encoded data symbols. A derived data symbol is thus represented by a transition from one differentially encoded data symbol to a next successive differentially encoded data symbol. The differentially encoded data symbols are then mapped onto the PSK constellation diagram. On the receiving side, the received differentially encoded data symbols are observed. Differential decoding is performed, wherein a differentially decoded data symbol is derived from a transition from one differentially encoded data symbol to a next differentially encoded data symbol. In other words, transmitted derived data symbols are represented by phase changes between successive differentially encoded data symbols.
An optical transmission channel may cause a phase error of the optical transmission signal. If, for example, the phase error exceeds from one data symbol to a next successive data symbol a value that is greater than half of the separation angle, then the next successive data symbol derived by differential decoding and by a hard decision detection scheme is erroneous. If further on, the phase error remains to be greater than the mentioned value, then further successive data symbols derived by differential decoding and by hard decision detection are correct. Thus, differential coding helps to reduce the impact of phase errors caused by a transmission channel in case of a hard decision detection scheme.